Probability of independent events

Probability is everywhere in our daily life. Do you know your chances of winning a specific prize in a spinning wheel prize draw? How about the odd to get the same prize two times in a row? By applying the concept of probability of independent events, we can easily answer these questions.

A spinner divided in 4 equal sections is spun. Each section of the spinner is labeled 1, 2, 3, and 4. A marble is also drawn from a bag containing 5 marbles: one green, one red, one blue, one black, and one white. Find the probability of:

a)

Landing on section 2 and getting the green marble.

b)

Not landing on section 3 and not getting the black marble.

c)

Landing on section 1 or 4 and getting the red or blue marble.

d)

Landing on any section and getting the white marble.

2.

A coin is flipped, a standard six-sided die is rolled; and a spinner with 4 equal sections in different colours is spun (red, green, blue, yellow). What is the probability of:

a)

Getting the head, and landing on the yellow section?

b)

Getting the tail, a 6 and landing on the red section?

c)

Getting the tail, a 2 and not landing on the blue section?

d)

Not getting the tail; not getting a 3; and not landing on the blue section?

e)

Not getting the head; not getting a 5; and not landing on the green section?

3.

A toy vending machine sells 5 types of toys including dolls, cars, bouncy balls, stickers, and trains. The vending machine has the same number of each type of toys, and sells the toys randomly. Don uses a five-region spinner to simulate the situation. The results are shown in the tall chart below:

Doll

Car

Bouncy Ball

Sticker

Train

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a)

Find the experimental probability of P(doll).

b)

Find the theoretical probability of P(doll).

c)

Compare the experimental probability and theoretical probability of getting a doll. How to improve the accuracy of the experimental probability?

d)

Calculate the theoretical probability of getting a train 2 times in a row?